If you are signed-in to the Amazon Chime iOS app using an Amazon account, you can delete you account from the Setting page. This is not applicable to Android, and does not apply to Enterprise accounts.
To do this:
1) Sign-in to the Amazon Chime iOS app with your Amazon account.
2) Go to 'Settings'
3) Tap 'Delete account'
4) You will be redirect you to a webpage to 'Close you Amazon account'. (Applicable to iOS only, and does not apply to other Enterprise accounts)
Important Note: Closing your Amazon account is permanent and applies to all Amazon products and services associated with the account.